Self-consistent calculation of particle-hole diagrams on the Matsubara frequency: FLEX approximation

TL;DR

This paper implements a numerical method for summing Green function diagrams in the FLEX approximation on the Matsubara frequency axis, applying it to the Hubbard model near half filling to analyze particle-hole dynamics and self-energy structures.

Contribution

The paper introduces a self-consistent numerical algorithm for FLEX calculations on the Matsubara frequency axis, applied to the Hubbard model near half filling, revealing detailed Green function and self-energy features.

Findings

Identification of three branches related to a two-peak structure in the self-energy

Confirmation of Fermi liquid behavior at the studied temperature

Comparison showing differences between fully self-consistent and non-selfconsistent approaches

Abstract

We implement the numerical method of summing Green function diagrams on the Matsubara frequency axis for the fluctuation exchange (FLEX) approximation. Our method has previously been applied to the attractive Hubbard model for low density. Here we apply our numerical algorithm to the Hubbard model close to half filling ($\rho = 0.40$), and for $T/t = 0.03$, in order to study the dynamics of one- and two-particle Green functions. For the values of the chosen parameters we see the formation of three branches which we associate with the a two-peak structure in the imaginary part of the self-energy. From the imaginary part of the self-energy we conclude that our system is a Fermi liquid (for the temperature investigated here), since Im$\Sigma(\vec{k},\omega) \approx w^2$ around the chemical potential. We have compared our fully self-consistent FLEX solutions with a lower order approximation where the internal Green functions are approximated by free Green functions. These two approches, i.e., the fully selfconsistent and the non-selfconsistent ones give different results for the parameters considered here. However, they have similar global results for small densities.